UPMSP Intermediate Logic common mistakes
UPMSP Intermediate Logic · Understand the traps and how to avoid them.
When asked to identify the logical form of an argument, the candidate labels any argument with an 'if...then' premise as modus ponens, even when the second premise affirms the consequent or denies the antecedent.
Candidates memorize the names of valid forms but do not check the direction of inference. They see a conditional and a second premise and assume it must be the familiar valid pattern, ignoring whether the second premise matches the antecedent or the consequent.
What to do instead
Before naming a form, write the conditional in symbols (p → q). Then write the second premise and conclusion in symbols. Check: does the second premise affirm p, deny p, affirm q, or deny q? Only affirm p (modus ponens) and deny q (modus tollens) are valid. Drill with mixed examples where the invalid forms (affirming the consequent, denying the antecedent) are deliberately included.
In a categorical syllogism, the candidate identifies the middle term incorrectly, often choosing the term that appears in the conclusion rather than the one that appears in both premises but not the conclusion.
Candidates rush to find the subject and predicate of the conclusion and assume the remaining term is the middle. They forget that the middle term must be distributed at least once and must not appear in the conclusion. This leads to wrong mood and figure, and thus wrong validity judgment.
What to do instead
Always label the conclusion first: identify its subject (minor term) and predicate (major term). Then scan the premises: the term that occurs in both premises but not in the conclusion is the middle term. Write the mood (e.g., AAA) and figure (based on middle term position) before checking validity with rules or Venn diagrams.
When converting a categorical proposition (e.g., 'All S are P') for immediate inference, the candidate treats conversion as always valid, producing 'All P are S' and calling it an equivalent.
Candidates confuse conversion with obversion and forget that A propositions convert only by limitation (to I) and O propositions do not convert at all. They apply the simple reversal of subject and predicate without checking the quality and quantity rules.
What to do instead
Memorize the conversion table: E and I convert simply; A converts by limitation to I; O cannot convert. For obversion, change quality and replace predicate with its complement (valid for all four). Practice by taking each proposition type and writing its converse, obverse, and contrapositive, then checking with a Venn diagram.
In predicate logic, the candidate translates 'All students are intelligent' as ∃x (Sx → Ix) or 'Some students are intelligent' as ∀x (Sx → Ix), swapping the quantifier and connective.
Candidates memorize that 'all' goes with arrow and 'some' goes with ampersand, but under exam pressure they invert them. They also fail to see that the wrong translation changes truth conditions: ∀x(Sx → Ix) is true if there are no students, while ∃x(Sx ∧ Ix) requires an existing student.
What to do instead
Use the rule: universal affirmative = ∀x(Sx → Px); particular affirmative = ∃x(Sx ∧ Px). Test with a scenario where there are no S: the universal is vacuously true, the particular is false. Also translate negative statements: 'No S are P' = ∀x(Sx → ¬Px); 'Some S are not P' = ∃x(Sx ∧ ¬Px). Practice with ten sentences and check each with a counterexample.
The candidate evaluates an inductive argument by asking whether the conclusion follows with certainty, and rejects strong inductive arguments as invalid because the conclusion could be false.
Candidates carry over deductive standards (validity, certainty) into inductive reasoning. They do not distinguish inductive strength from deductive validity, and they forget that inductive arguments are assessed by probability, not necessity.
What to do instead
Learn the distinct criteria: deductive arguments are valid/invalid (conclusion follows necessarily); inductive arguments are strong/weak (conclusion follows probably). For a strong inductive argument, the premises make the conclusion likely, not certain. Practice classifying arguments as deductive or inductive first, then apply the correct standard.
In Nyaya logic, the candidate lists the five members of a syllogism (pratijna, hetu, udaharana, upanaya, nigamana) but misidentifies the hetu (reason) as the paksha (subject) or confuses the upanaya with the nigamana.
Candidates memorize the names in order but do not understand the function of each member. They especially confuse the upanaya (application) with the nigamana (conclusion), and they may think the hetu is the conclusion because it contains the reason.
What to do instead
Map each member to its function: pratijna = thesis (the claim to be proved); hetu = reason (the evidence); udaharana = example (a familiar instance); upanaya = application (asserting the example applies to the present case); nigamana = conclusion (restating the thesis as proved). Use a standard example (e.g., 'The hill has fire because it has smoke, like a kitchen, so this hill has fire, therefore the hill has fire') and label each part. Practice with new examples.
When defining a term, the candidate offers a definition that is too broad or too narrow, or uses the term itself (circular), and still marks it as correct.
Candidates focus on giving a dictionary-like definition but do not test it against the rules of good definition: extend the definiendum and definiens to see if they match. They also overlook that a definition must not be figurative or negative when it can be positive.
What to do instead
Apply the five rules of definition: (1) state the essential attributes; (2) do not be circular; (3) not too broad or too narrow; (4) avoid ambiguous, obscure, or figurative language; (5) not negative if affirmative is possible. For each definition, test by asking: does the definiens include all and only the things the definiendum denotes? Practice with examples of faulty definitions and correct them.
In propositional calculus, the candidate uses truth tables to test validity but makes errors in assigning truth values to complex formulas, especially with conditionals and biconditionals, and thus misclassifies a tautology as contingent.
Candidates are careless with the truth conditions of the conditional (false only when antecedent true and consequent false) and the biconditional (true when both sides have the same truth value). They also forget to evaluate the main connective last, leading to wrong column readings.
What to do instead
Before building a truth table, identify the main connective. Build the table step by step, writing subformula columns. For the conditional, remember 'false only when T → F'. For the biconditional, 'true when same'. After completing, check the main column: all T = tautology, all F = contradiction, mixed = contingent. Practice with ten formulas of varying complexity and verify with a second method (e.g., shortcut method).
The candidate treats the fallacy of affirming the consequent as valid because the conclusion seems plausible, or confuses it with modus ponens when the conditional is stated in reverse order (e.g., 'If it rained, the ground is wet; the ground is wet; therefore it rained').
Candidates rely on everyday plausibility rather than logical form. They do not translate the argument into symbols and check the pattern. The reversed order of the conditional (consequent first) makes the fallacy less obvious.
What to do instead
Always symbolize the argument. For 'If it rained, the ground is wet' use R → W. The second premise 'the ground is wet' is W (the consequent). Affirming the consequent is invalid. Test with a counterexample: sprinklers could make the ground wet. Practice distinguishing modus ponens (affirm antecedent), modus tollens (deny consequent), affirming consequent (invalid), denying antecedent (invalid).
In the nature and scope of logic, the candidate claims that logic is the science of the laws of thought and that it studies how people actually think, rather than the normative study of correct inference.
Candidates confuse descriptive psychology with normative logic. They repeat the popular phrase 'laws of thought' without understanding that logic prescribes how one ought to reason, not how one does reason. This leads to wrong answers about the scope of logic and its relation to psychology.
What to do instead
Learn the standard distinction: logic is the normative science of valid inference; it studies the form of arguments, not the actual psychological processes. Psychology describes thinking; logic prescribes correct thinking. Also note that logic is not concerned with the content of thoughts but with their structure. Review definitions from standard textbooks and practice distinguishing logical questions from psychological ones.